Consider a project of manufacturing and selling high$-$end smartwatches to wealthy customers. The length of the project is $10$ years. The industry demand for high$-$end smartwatches next year will be $1$ million units, and every year it will either increase by $3\%($with $50\%$ probability$)$ or decrease by $3\%($with $50\%$ probability$).$ Your market share next year will be $5\%,$ and every year it will either increase by $1\%-$point $($with $50\%$ probability$)$ or decrease by $1\%-$point $($with $50\%$ probability$),$ but your maximum capacity of annual production is $100,000$ watches per year. $($I$.$e$.,$ if your market share would grow to a level which would require producing more than $100,000$ watches per year, it will be capped at the level corresponding to $100,000$ watches per year. Then, next year, it will again either increase by $1\%-$point or decrease by $1\%-$point, with the same capacity constraint being in effect.$)$ The initial cost of the project is $$10$ million, which is used to purchase the equipment necessary to manufacture smartwatches. This initial cost is amortized over a $5-$year period using the straight$-$line method. Every year, the annual inflation will be either $1\%($with $50\%$ probability$)$ or $2\%($with $50\%$ probability$).$ In the first year, fixed costs will be $$100,000,$ and every year they will increase by the inflation. In the first year, variable costs will be $$200$ per unit, and every year they will increase by the inflation. If your market share drops to $0\%,$ you abandon the project and sell your equipment for its book value or $20\%$ of its initial price $($whichever is higher$).$ At the end of the $10$th year, you sell the equipment for $20\%$ of its initial price $($if you have not sold it earlier already$).$ The price at which you can sell the watches depends on the industry$-$wide demand in that year $($a higher demand leads to a higher price$).(60$ points$)$ Consider a project of manufacturing and selling high$-$end

smartwatches to wealthy customers. The length of the project is $10$ years. The

industry demand for high$-$end smartwatches next year will be $1$ million units, and

every year it will either increase by $3\%($with $50\%$ probability$)$ or decrease by $3\%$

$($with $50\%$ probability$).$ Your market share next year will be $5\%,$ and every year it will

either increase by $1\%-$point $($with $50\%$ probability$)$ or decrease by $1\%-$point $($with

$50\%$ probability$),$ but your maximum capacity of annual production is $100,000$

watches per year. $($I$.$e$.,$ if your market share would grow to a level which would

require producing more than $100,000$ watches per year, it will be capped at the

level corresponding to $100,000$ watches per year. Then, next year, it will again

either increase by $1\%-$point or decrease by $1\%-$point, with the same capacity

constraint being in effect.$)$ The initial cost of the project is $$10$ million, which is

used to purchase the equipment necessary to manufacture smartwatches. This

initial cost is amortized over a $5-$year period using the straight$-$line method. Every

year, the annual inflation will be either $1\%($with $50\%$ probability$)$ or $2\%($with $50\%$

probability$).$ In the first year, fixed costs will be $$100,000,$ and every year they will

increase by the inflation. In the first year, variable costs will be $$200$ per unit, and

every year they will increase by the inflation. If your market share drops to $0\%,$ you

abandon the project and sell your equipment for its book value or $20\%$ of its initial

price $($whichever is higher$).$ At the end of the ${10}^{th}$ year, you sell the equipment for

$20\%$ of its initial price $($if you have not sold it earlier already$).$ The price at which you

can sell the watches depends on the industry$-$wide demand in that year $($a higher

demand leads to a higher price$).$ Namely, the price per unit is equal to

$\frac{\text{i}\text{n}\text{d}\text{u}\text{s}\text{t}\text{r}\text{y}\text{d}\text{e}\text{m}\text{a}\text{n}\text{d}}{4000}+x,$ where $x$ is a random number taking a value in the interval

$-50,50$ and it follows a uniform distribution $($i$.$e$.,$ it takes all value within the given

interval with equal likelihood$).$ In any case, the unit price never drops below the

actual variable costs per unit. $($I$.$e$.,$ if the unit price would be lower than the variable

costs per unit based on the above formula, then the unit price will be equal to the

variable costs per unit.$)$ The corporate tax rate is $25\%.$ Assu